Fuel is actually comparably priced for a biker because you burn food. Some people don't have this problem. However, lets say a gallon of gas runs you $4 and gets you 40 miles. What would you eat for $4 that will power you for 40 miles on a bike?

I also don't completely buy the oil change thing either. If you are financially at the point where you are looking to save money riding a bike, you have long since given up on newer cars and professional oil changes. You are driving a beater that might not make it to the next oil change, and if you do change it yourself, it's going to get the cheapest oil/filter you can find.

The tire thing is about even. Four cheap tires for the car might cost $400 and go 40,000 miles. If you get 4000 miles out of a set of bike tires, you'd need ten sets at $40/set to match the cost of car tires.

As you say, it all depends on what you spend. I'm just pointing out the fallacy of assuming cycling is necessarily cheaper.